Stats Unit 1

research

the systematic investigation into and study of materials and sources to establish facts and reach conclusions

observational research

investigator measures relationships between events or conditions but does not manipulate or intervene

experimental research

investigator directly manipulates conditions (cause) to measure the response (effect)

data

results of repeated measurements

data must be

reliable, valid, objective

discrete variables

limited to certain values; counted

continuous variables

can theoretically assume any value; measured

nominal scale

mutually exclusive categories, no logical order

ordinal scale

logical order, but no indication of size of difference (rank order)

interval scale

equal intervals, but no “absolute” zero

ratio scale

equal intervals and an “absolute” zero

intervening/confounding variables

uncontrolled variables that influence dependent variables

internal validity

result observed in the DV is entirely due to the treatment

ways to achieve internal validity

use a control group, minimize instrument error, minimize investigator error

external validity

the result can be generalized to the wider world

ways to achieve external validity

random sampling and do not control everything

sample

a portion of the larger population that is assumed to represent the population

random sample

each member of the population has an equal chance of being selected

stratified sample

ensure representation of subgroups within the population of interest

convenience sample

members are selected based on “ease and proximity”

parameter

characteristic of a population; set limits to study

statistic (object)

sample characteristic used to estimate a parameter of the population

statistics (field)

science of inferring proportions in a population from a representative sample

percentiles

provide a comparison to the range of scores/characteristics obtained from the larger sample or population

percentiles purpose

allow for evaluation of raw scores and comparison between different units of measurements

probability

the long-run proportion of a particular outcome

classical probability

the likelihood of a prticular outcome within a finite set of mutually exclusive, equally likely possible outcomes

frequentist probability

the long-run tendency toward a particular outcome within many trials

p-value

the likelihood that the resolts are due entirely to chance

subjective probability

based on a degree of belief

measures of central tendency (def)

values that describe the middle characteristics of a dataset

measures of central tendency

mean, median, mode

when to use the mean

interval and ratio data type with no skew/outliers

median

the middle score in a ranked ordered list of scores; splits the dataset into equal halves

when to use median

ratio, interval, and ordinal data types that is skewed/ has outliers

mode

score that occurs most frequently

when to use mode

nominal or ordinal data

measures of variability (def)

quantify the dispersion or spread within a dataset

measures of variability

range, IQR, variance, standard deviation

when to use range

interval and ratio data

limitations to range

sensitive to outliers, says nothing about pattern

when to use IQR

ordinal, interval, and ratio data (heavily skewed)

limitations to IQR

says nothing about the pattern

standard deviation

square root of the sample variance

when to use SD

interval and ratio data

coefficient of variation

percentage that allows comparison of variability between different variables

central limit theorem

the distribution of sample means will be normally distributed, regardless of the original population's distribution, as long as the sample size is sufficiently large

bimodal distribution

poisson distribution

log normal distribution

power law

standard scores

scores derived from raw data with a known basis for comparison

what to use standard scores for

compare between datasets with different units

Z-scores

express the raw score in standard deviation units

T-scores

converted z-score to be more intuitive

skewness

asymmetry of distribution

positive skew

mode is shifted leftward

negative skew

mode is shifted rightward

how to convert skewness scores to z-scores

divide skewness by standard error

normal skewness z-score

±1.96

kurtosis

the “steepness” of the distribution

platykurtic

wide range of scores, low concentration around mean

leptokurtic

narrow range, high concentration around mean

mesokurtic

moderate range, moderate concentration around mean

more variability means

greater difference in means needed to achieve significant differences

Q-Q plots

plots the quantiles of the dataset against the theoretical quantiles of a normal distribution

normal Q-Q plot

skewed to the right Q-Q plot

heavy tail (platykurtic) Q-Q plot

light tails (leptokurtic) Q-Q plot

skewed to the left Q-Q plot

Shapiro-Wilk and Kolmogorov-Smirnov tests

tests that sample does not follow normal distribution

when to use K-S test

samples > 50

when to use S-W test

samples < 50